I found a great website that explains how to cure hyperthyroidism and hypothyroidism. Both can be cured by correcting the nutrient imbalances of the body that are unique to each problem.
I can't remember if it mentions this on that website or not, but I just want to add that in my experience, magnesium citrate is helpful as well. Especially for hyperthyroid.
For hyperthyroid I ate a few tablespoons of blackstrap molasses each day, which definetly helped. As an alternative to supplements, it contains copper and magnesium that are needed for hyperthyroidism.